带有互助保险的二元复合非齐次Poisson风险模型

Binary Composite Non-homogeneous Poisson Risk Model with Mutual Insurance

考虑在二元Cramér-Lundberg风险过程下,保险公司索赔到达率服从非齐次Poisson过程,且两个保险公司之间拥有互相弥补亏损协议,用鞅方法得到一元风险过程有限时间破产概率的一个上界;结合二元生存概率Laplace变换的核方程,得到二元Cramér-Lundberg风险过程下两个保险公司生存概率的一个下界;最后,给出了两个保险公司险种的个体索赔额均服从指数分布时生存概率的下界估计,为保险公司预留必要的准备金提供参考。

Considering the process of dualistic Cramér-Lundberg risk,the claim arrival rate obeys the non-homogeneous Poisson process,and the two insurers have mutual compensation agreements. The upper bound of the finite time ruin probability of the unary risk process is obtained by martingale method. Combining the kernel equation of the binary survival probability Laplace transform,we obtain a lower bound of the survival probability of the two insurers under the dual Cramér-Lundberg risk process.The lower bound estimate of the survival probability of two insurance companies when the individual claim amount is exponentially distributed is given,which provides a reference for the insurance companies to reserve necessary reserves.